“Second star to the right and straight on ‘til morning.” I’m pretty sure that if most people now took Peter Pan’s directions to Neverland, they’d never get there. In these modern times, we rely significantly less on the sky to navigate and it’s only because of the knowledge accumulated and developed over time. Finding new information usually isn’t an easy task without using prior knowledge of another subject or idea as a starting point. For example, astronomical observations used known mathematics to become more pertinent to modern-day science. Such was the case for China, as time was measured and kept constant with the usage of the cycles of the sun and moon as well as intercalation– the insertion of days and months to make the lunisolar calendar follow the moon phases. The study of the night sky flourished for the Chinese during the Han dynasty (206 BCE – 220 CE), continuing through to the modern day.
The lunisolar calendar was used to mark the passing of the seasons and special occasions. The Chinese used advanced algebra for this purpose. It was mainly equatorial based, which focused on circumpolar stars and ecliptic frameworks that stemmed from Western science. The Zhou Bi Suan Jing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven), one of the oldest and most famous Chinese mathematical texts dating back to the Zhou dynasty (1046 BCE – 256 BCE), used the Pythagorean Theorem on astronomical calculations as well as for multiple equatorial based problems. To go into detail, one of the 246 problems in the compilation was to find the height of the sun from the earth, as well as the diameter of the sun. One person was to wait until the shadow of a 264 cm gnomon (the part of a sundial that casts the shadow) was 198 cm so that a large 3-4-5 right-angle triangle could be formed. This larger triangle would be from the sun straight to the ground, along the ground to the gnomon (forming the right-angle), and from the gnomon to the sun (angle of elevation). The smaller triangle, consisting of just the gnomon and its shadow, was used to find the equivalent measurements of the larger triangle so that the Pythagorean Theorem could be applied. As a result to this problem, the base of the triangle would be 24,900,000 m, the height of the sun 33,200,000 m, and the hypotenuse going toward the sun 41,500,000 m.
Moving through to the Tang dynasty (618 CE – 907 CE), Yi Xing was a well-known monk, engineer, and astronomer who had used the knowledge of the previous dynasty to work on an astronomical clock, which displayed the relative positions of the sun, moon, zodiacal constellations and major planets occasionally. The improvements on the function of an astronomical clock would later be succeeded by Su Sung during the Song dynasty (960 CE – 1279 CE), when he created a water-driven astronomical clock for his clocktower, and designed and constructed a Cosmic Engine that operated as an astronomical hydromechanical clock tower. Su Sung had worked off of the achievements of Zhang Heng, an astronomer, inventor, and guru of mechanical gears who lived from 78 CE – 139 CE. Along with that, Su Sung was among the first during the dynasty to work on empirical science and technology.
Another genius during this time was Shen Kuo, who was most known for finding the concept of the geographic north pole (true north) and the magnetic declination (angle on the horizontal plane between magnetic north and true north) towards the north pole by using a more precise measurement of what’s known as the astronomical meridian (a large circle that passes through the celestial poles, the nadir (vertical direction pointing in the direction of the force of gravity), and the zenith (vertical direction opposite to the force of gravity, opposite of the nadir) for a given location). He also used advanced math to calculate the position of the pole star that had moved over many centuries, which made sea navigation more accurate using a magnetic needle compass. Shen Kuo also theorized that the sun and moon were both spherical and used cosmological hypotheses to predict planetary motion. He worked with his colleague, Wei Pu, to record and plot the moon’s orbital path for a duration of five years. However, much of their efforts were wasted thanks to political rivals who only used part of the corrected plots calculated by Shen Kuo and Wei Pu for planetary orbital paths and speeds.
The Song dynasty was followed closely by the People’s Republic of China from 1912 to modern-day, during the time of rapid development in science and technology. They moved away from the study of celestial objects and focused more on the application of past astronomical studies on mechanical technology and modern science. So where the use of calculation, measurement, and logic was previously aimed toward the shapes and motions of celestial objects, it was now applied to military technology, arsenals, shipyards, steamships, and artillery. In short, the Chinese did not reduce observations of nature to mathematical laws until much later, since for a short period after the Song dynasty the focus was mainly on literature, arts, and public administration. Chinese mathematics had shifted more towards Western mathematics in terms of being used for technology and modern science rather than for astronomical studies. Despite this, China and many other Asian cultures still use the lunisolar calendar, remade each year using the same mathematical calculations from the Han dynasty.